The prediction model of coal reservoir pressure and its ... YAN, Songha… · Running title: The prediction model of coal reservoir pressure and its implication The prediction model

Running title: The prediction model of coal reservoir pressure and its implication

The prediction model of coal reservoir pressure and its implication for the law of coal

reservoir depressurization

Xinlu YAN 1,2,3

, Songhang ZHANG 1,2,3,*

, Shuheng TANG 1,2,3

,Zhongcheng LI4， Kaifeng WANG 1,2,3, Yongxiang YI 1,2,3 , Feng

DANG 1,2,3

and Qiuping HU4

1. School of Energy and Resources, China University of Geoscience, Beijing, 100083, China

2. MOE Key Lab of Marine Reservoir Evolution and Hydrocarbon Accumulation Mechanism, China University of Geoscience, Beijing, 100083,

China

3. Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, Beijing, 100083, China

4. China United Coalbed Methane Corporation Ltd, Beijing, 100011, China Abstract：The main methods of coalbed methane (CBM) development are drainage and depressurization. Therefore, precise prediction of coal reservoir pressure is crucial for the evaluation of the reservoir potentials and the formulation of reasonable development plans.

In this paper, a new reservoir pressure prediction model was established basing on the material balance equation (MBE) of coal reservoir; the model

considers coal reservoir self-regulating effects and dynamic change of equivalent drainage area (EDA). According to the proposed model, the

reservoir pressure can be predicted based on the reservoir condition data and on the actual production data of a single well. Compared with the

traditional reservoir pressure prediction models, where EDA is considered as a fixed value, the proposed model shows a more reasonable prediction

of the reservoir average pressure. Moreover, in the proposed model, orthogonal experiments were designed to evaluate the sensitivity of the reservoir

parameters on the reservoir pressure prediction results. The results showed that the irreducible water saturation is the most sensitive parameter, which

is followed by the Langmuir volume and the reservoir porosity; the Langmuir pressure is the least sensitive parameter. In addition, we found that the

reservoir pressure drop is negatively correlated with the irreducible water saturation and the Langmuir volume, while it is positively correlated with

the porosity. By analyzing the reservoir pressure drop characteristics of the CBM wells in the Shizhuangnan Block, in the Qinshui Basin, the results

showed that the CBM reservoir depressurization can be divided into three types, which are the "rapidly drop type", the "medium-term stability type",

and the "slowly drop type". The drainage features of wells were reasonably interpreted based on the comprehensive analysis of the reservoir

depressurization type; the latter was coupled to the corresponding permeability dynamic change characteristics, eventually proving the applicability

of the proposed model.

Keywords: coalbed methane, pressure prediction, equivalent drainage area, influencing factors, pressure drop types

E-mail：[email protected]

This article is protected by copyright. All rights reserved.

This article has been accepted for publication and undergone full peer review but has not been

through the copyediting, typesetting, pagination and proofreading process, which may lead to

differences between this version and the Version of Record. Please cite this article as doi:

10.1111/1755-6724.13869.

https://doi.org/10.1111/1755-6724.13869https://doi.org/10.1111/1755-6724.13869https://doi.org/10.1111/1755-6724.13869

Nomenclature

the equivalent drainage area final reservoir pressure

gas volume coefficient at initial pressure reservoir pressure variation

gas volume factor the standard pressure

water formation volume coefficien coal density formation water compressibility coefficient reservoir pressure drop rate

buried depth of coal seam the initial water saturation of the original fissure Young modulus the irreducible water saturation

the maximum volumetric strain reservoir temperature the surface volume of cumulative gas production the standard temperature

coal seam thickness the Langmuir volume bulk modulus actual gas content

permeability poisson’s ratio axial modulus of elasticity the surface volume of cumulative water production

reservoir pressure the standard deviation factor of gas the critical reservoir pressure the initial porosity

the initial reservoir pressure porosity

the Langmuir pressure

1 Introduction

The energy demand is increasing worldwide (Chu and Majumdar, 2012). As an unconventional new energy source, coalbed

methane (CBM) increasingly plays an important role in fossil energy (Kuuskraa, 1989; Clarkson and Salmachi, 2017). The Qinshui Basin, as the CBM test area in China, has been commercially developed (Su et al., 2005; Jian et al., 2012). The coal reservoir in the Qinshui Basin is an undersaturated coal seam (Su et al, 2004), and the production process can be divided into three stages; the stages are: saturated single-phase water flow, unsaturated single-phase water flow, and gas/water two-phase flow (Tang et al., 2015). The main development methods of CBM in the Shizhuangnan Block are drainage and depressurization (Cervik, 1969; Salmachi and Yarmohammadtooski, 2015). As unsaturated CBM reservoirs do not produce commercial quantity gas until the reservoir pressure drops below the critical desorption pressure, the production wells must experience a long water drainage and an unstable gas production stage (Carlson, 2006). Therefore, the full depressurization of the coal reservoir is the key to CBM production during the development process.

At present, there are two main methods to calculate the reservoir pressure. In the first method, the pressure propagation law is calculated through the seepage equation (Zhao and Zhang, 2012; Liu et al., 2012; Zhang et al., 2017; Sun et al., 2017; Sun et al., 2018). Using the seepage equations to calculate the reservoir pressure aims to establish a mathematical model for coal seam pressure distribution on one hand, and to combine the reservoir permeability data and the water production date during the production process on the other. The advantage of this method is that the dynamic change of the drainage range is considered; furthermore, the change of the reservoir pressure is calculated in different regions during the production process. However, the strong heterogeneity of the coal reservoir, the large inaccuracy in the permeability parameters, and the underutilization of gas production date cause inaccuracy in the pressure calculation. In the second method, the average pressure of coal reservoir is obtained by using the coal reservoir material balance equation (MBE) combined with the basic parameters of the reservoir and the actual production data. King (1993)

first

established the MBE for CBM, which was later improved by subsequent studies. Penuela et al. (1998) developed a generalized MBE for CBM reservoirs in which the diffusion process of desorbed gas into cleat system was considered. Moreover, Ahmed et al. (2006) proposed a generalized MBE that considered the initial free gas, water expansion, Langmuir isotherm, and formation compaction to estimate the original gas in place. Afterward, Hu and Li (2010) classified the coal seam as a dual-medium of matrix and cracks; they proposed an improved MBE that involves the self-regulating effects of coal seams. Then, Zhao et al. (2014) established a new MBE for undersaturated low rank CBM; on this basis, the dynamic change of the relative permeability was calculated. Additionally, Thararoop et al. (2015) developed a new MBE for CBM reservoirs that considered the water presence in the coal matrix as well as coal shrinkage and swelling. More recently, Shi et al. (2018) developed the MBE that considers the effects of various factors, such as the difference between the initial reservoir pressure and the critical desorption pressure, pore compressibility, water compressibility, coal matrix shrinkage, dissolved gas, and free gas. The MBE for CBM is developed to predict the single well controlled area and the original gas in place. The advantages of using the MBE method to calculate the average reservoir pressure is to make full use of the production data, and the requisite geological parameters of coal reservoir are more accurate. Unfortunately, previous studies did not consider the dynamic change of the drainage area when calculating the average reservoir pressure. That is, the drainage area is artificially set rather than setting the actual scope of the development process; this means that the calculated reservoir pressure might be untrue.

To solve the limitations of the CBM material balance equation, a new reservoir pressure prediction model was established based on the MBE of coal reservoir in this study. It is worth noting that the proposed model takes into consideration the coal reservoir self-regulating effects and dynamic change of the equivalent drainage area (EDA). Fourteen wells from the Shizhuangnan Block in the southern Qinshui Basin in China were employed for a case study. The dynamic average reservoir pressure during the CBM production was acquired by using production date based on the proposed reservoir pressure calculation model. Taking the well T1 among 14


wells as an example, the difference between the traditional model and the proposed model was analyzed, and the influence of the geological factors on reservoir pressure was further studied.

2 Regional Geology 2.1 Geological characteristics in the Shizhuangnan Block

The Shizhuangnan Block is located in the southern region of the Qinshui Basin, Shanxi Province. The entire field is made from tectonic rocks that slope westward, and its structure is simple. The Qinshui Basin is mainly filled with Permo–Carboniferous sediments (Yao et al., 2008). The strata in the study area include Cambrian, Ordovician, the Carboniferous Benxi (C2b) and Taiyuan (C3t) Formations, the Permian Shanxi Formation (P1s), the Xiashihezi Formation (P1x), the Shangshihezi Formation (P2s), the Shiqianfeng Formation (P2sh), the Triassic Liujiagou Formation (T1l), and Quaternary deposits. The C2b unconformably overlies on the Ordovician Formation (Zhang et al., 2015). The main coal-bearing strata are the upper Carboniferous Taiyuan Formation (C3t) and the lower Permian Shanxi Formation (P1s), which contain the coal seam No.15 and No.3, respectively (Yang et al., 2017). The total thickness of the two coal seams is 10.7 meters. At present, the mine-field mainly produces No.3 coal seams which mainly consists of anthracite; its coal vitrinite reflectance (Romax) ranges from 2.92% to 3.02%. The No.3 coal seam is stable and the thickness ranges from 4.45 to 8.75 m, with an average of 6.35 m. The shallowest and deepest depths of this coal seam are 451 and 1030 m, respectively (Zhu et al., 2017). It is generally deeper in the northern and the central regions, while it is shallower in the southern and the eastern regions. The gas contents of the coal range between 13 and 20 m3/t. The gas contents in the west and in the north are bigger than the contents in the east and in the south (Yan et al., 2018).

Fig.1 Location of the sampling and study area. (a) Location of the study area in China (China basemap after China National Bureau of Surveying and Mapping Geographical Information); (b) The study area, showing

CBMBlocks in the southern Qinshui basin; and (c) structure outline of the study area and the wells where water samples were collected. SZN, Shizhuangnan CBM Block; MB,

Mabi CBM Block; ZZ, Zhengzhuang CBM Block; FZ, Fanzhuang CBM Block; PZ, Panzhuang CBM Block).

2.2 Basic parameters for the reservoir pressure calculation

Some production wells were selected as target wells in the Shizhuangnan Block of the Qinshui Basin; the locations of these wells are shown in figure 1. These wells are characterized by continuous gas production; the initial artificial fracture of these wells is effective from the hydraulic fracturing report, meaning that there are no external causes to stop production. Peng et al. (2017) established a prediction model for the CBM content by matching isothermal adsorption experiments and log interpretation in the Shizhuangnan Block. Consequently, the gas content of each production well was calculated by the combination of the log interpretation data of production wells and previous research results. The specific parameters of each well are shown in Table 1. The production time for all the production wells is more than 1500 days, while it is more than 2000 days for 9 of these production wells (Table 2); this indicates that the production status of the selected production wells is basically stable. According to the average gas production rate, the production wells are classified as high (>1000 m

3/d), medium (500-1000 m

3/d), and low (＜500 m3/d) gas-yield

production wells. The 14 production wells can be divided into three groups; 4, 5, and 5 have high, medium, and low gas-yield production wells, respectively, with averages of 1680.5 m

3/d, 669 m

3/d, and 251.9 m

3/d, respectively. The daily water production rate

ranges between 0.52 and 2.27 m3/d. The cumulative water yield of each well is low during the production process, which indicates that

the CBM wells produce coal seam water and that there is no influence of inrushing water (Li et al., 2018). Other basic parameters can be obtained through well logging and well testing; for a wellbore of 0.1m radius, the water

compressibility of MPa-1, the water formation volume factor of 1m3/m3, the dimensionless maximum Langmuir volumetric strain of 1.25%, the initial water saturation of 0.95, and the Young modulus of 4300 MPa

-1can be obtained. Shen et al.

(2011) measured the irreducible water saturation of coal seams to be approximately 0.6 by physical simulation experiments on coal samples from the southern Qinshui Basin.


Table 1 Basic parameters for the pressure prediction in the Shizhuangnan Block

Wells D(m) H(m) /(g/cm3) (MPa) (MPa) VL(m3) PL(MPa) (m

3/t) K(mD) T(℃)

T1 776.10 5.00 1.23 3.30 1.87 29.86 2.10 16.13 0.76 0.03 25 0.3

T2 735.80 6.50 1.48 3.34 1.76 32.73 3.40 14.08 0.13 0.01 24.5 0.38

T3 714.00 6.50 1.38 4.20 2.20 26.14 1.62 15.04 0.10 0.05 24.6 0.39

T4 718.0 6.10 1.30 3.61 1.21 36.00 1.70 14.98 0.42 0.04 21.4 0.33

T5 729.40 5.70 1.23 3.68 2.14 34.81 2.19 17.20 0.08 0.03 24.5 0.3

T6 767.00 5.90 1.40 3.42 2.06 33.00 2.25 15.77 0.80 0.05 25.5 0.3

T7 533.60 6.00 1.30 3.10 1.32 36.84 1.70 16.12 0.44 0.04 24 0.32

T8 716.30 5.40 1.51 3.20 1.84 34.00 2.30 15.11 0.28 0.05 23.7 0.27

T9 769.10 6.05 1.39 3.34 2.03 26.42 3.07 10.52 0.11 0.03 25.5 0.28

T10 717.20 5.66 1.35 2.63 1.94 26.71 2.80 10.94 0.38 0.04 22.4 0.31

Z1 607.70 5.80 1.42 3.30 2.07 35.71 1.80 19.07 0.25 0.03 23.3 0.3

Z2 698.50 6.30 1.39 4.37 2.17 36.00 2.38 17.15 0.07 0.04 23.4 0.3

Z3 711.65 6.00 1.32 4.32 1.82 36.26 1.50 19.88 0.12 0.04 24.2 0.33

Z4 717.20 6.30 1.42 3.35 1.50 33.51 2.99 11.19 0.36 0.04 24.3 0.33

Table 2 Production parameters of CBM wells

Wells Time (day) Average daily gas

Production (m3)

Average daily water

production (m3)

T1 2308 545.29 1.54

T2 1553 717.52 1.34

T3 1503 306.86 2.11

T4 1821 553.17 1.21

T5 2044 1081.83 0.52

T6 2341 1064.49 2.27

T7 2285 566.11 0.80

T8 1960 423.97 1.53

T9 2340 198.90 2.02

T10 1531 160.88 1.79

Z1 2622 1279.08 0.93

Z2 2476 2493.09 1.45

Z3 2520 1868.39 0.53

Z4 2240 168.80 1.73

3 Method

The calculation of the average pressure of the coal reservoir is based on the CBM material balance equation. However, the

traditional model has limitations (specific analysis in Section 4.1). Thus, we considered the dynamic change of the EDA basis on the previous model in this study; this makes the calculation results more accurate. There are three steps to improve the reservoir pressure calculation model; the first is to establish a gas-phase MBE in the production process based on the principle of volume conservation; the second is to change the form of the water-phase MBE so that the EDA increases with the water production; the last is to substitute the EDA formula into the gas-phase MBE. Therefore, the reservoir pressure calculation model, which considers the dynamic change of the EDA, can be deduced.

The CBM in the coal seams is mainly present in the form of adsorbed, free, and dissolved gas. However, the proportion of dissolved gas is very small (Dan et al., 1993; Meng et al., 2010); therefore, the dissolved gas is not taken into consideration when the gas-phase MBE is deduced. The ground volume of accumulated gas production is equal to the original geological reserves of the adsorbed gas in the matrix minus the remaining geological reserves of the adsorbed gas in the matrix plus the original geological reserves of the free gas in the fracture minus the remaining geological reserves of the free gas in the fracture (the gas volume is the volume under the ground condition.)

(Ahmed et al., 2006):

(1)

Moreover, the formation water in the coal seam mainly exists in fractures and pores. Due to changes in reservoir pressure, the water compressibility changes and elastic expansion occurs; this leads to an increase in the water volume (Zhao et al., 2014). According to the conservation principle of formation water volume, the remaining volume of formation water in the reservoir is equal to the water volume in the fracture in the original condition plus the water volume increased by elastic expansion minus the accumulated water production volume (the water volume is the volume of underground condition):

(2) With the increase of the drainage area, pressure dropping funnel continues to expand during the development process. When the

reservoir pressure drops below the critical desorption pressure, the absorbed gas starts to desorb within the coal reservoir affected by the pressure dropping funnel. If the pressure dropping funnel is considered an equivalent cylindrical geometry around the borehole,


then the EDA may be used to characterize the pressure drop area, and the quantity of gas desorption is closely related to the EDA (Tao et al., 2014).

Formula (2) can be transformed into:

[ ] (3)

By substituting the above EDA equation into the gas balance equation, the MBE of the coal reservoir can be obtained; this is considered the dynamic change of the EDA.

[ ( )

( )( )

( )

[ ] (4)

The gas volume factor ( ) varies during production and can be calculated by:

(5)

Where Z is the deviation factor of gas, which is assumed to be 0.864 due to its slight change during production, and T is the reservoir temperature. Since each well has a corresponding reservoir temperature, the gas volume factor is a function of reservoir pressure.

When the proposed model is applied to calculate the coal reservoir pressure, the dynamic change of the reservoir porosity should not be ignored. The dynamic change of the porosity during the development process is mainly divided into two stages. The first stage is the saturated single-phase water flow stage; during this stage, only the formation water discharges, the overlying stress of the reservoir increases, and the porosity decreases. The second stage is the gas-water two-phase flow; there is an effective stress effect at this stage. Simultaneously, the CBM desorbs from the coal matrix and causes coal matrix shrinkage. When the effective stress effect is greater than the matrix shrinkage effect, the porosity decreases, otherwise, it increases (Zhao et al., 2016).

{

(

) (

)

（6）

（7）

（8）

When we substitute equation (6) into (4), a coal reservoir pressure calculation model is obtained which involves the self-regulatory effect and variable EDA. Based on the production data and the reservoir geological parameters, the new reservoir pressure calculation model can be used to calculate the average reservoir pressure during the development process.

4、Results and Discussions 4.1 Reliability of the proposed model

King (1993) first established the MBE of coal reservoirs. Since then, the model was used to calculate the average reservoir pressure:

[ ]

(9)

The traditional reservoir pressure calculation model does not consider the dynamic change of the drainage area; instead, it substitutes the fixed value of the area into the calculation model. First, the fixed value of the area in the traditional model is the single well controlled range, and it refers to the well spacing. Furthermore, the well spacing is not the pressure drop range; meaning that the pressure drop range can’t be replaced by the well spacing. Second, the production system of the production well is the drainage and depressurization, and the drainage area continuously changes with the progress of production. If the fixed value of the area is substituted into the model instead of the dynamic drainage area when the reservoir pressure is calculated, the result will be irrational.

Taking the well T1 as an example, two models were used to calculate the reservoir pressure. The geological parameters of well T1 are shown in Table 1. The actual drainage curve of well T1 is shown in figure.2. When the traditional prediction model was used to calculate the reservoir pressure, the well-controlled radius was set to 100, 150, and 200 m. The calculation results of the average reservoir pressure for the two models are shown in figure.3.


Fig.2 Actual production curve of the T1 well.

Fig.3 Calculation of reservoir pressure by substituting different drainage area.

Fig.4 Sketch of pressure calculation range for two models.

When the dynamic EDA is not taken into account, the reservoir pressure calculation results by substituting the different drainage areas are quite different (Fig.3); the greater the drainage area, the slower the drop in the reservoir pressure. At about 750 days, the EDA reached 100 m. At that time, when the constant drainage radius was set to 100 m, the calculation result of the proposed model was the same as the traditional model. This indicates that if the fixed value of the area is smaller than the actual drainage range, the calculated reservoir pressure will greatly drop. Conversely, if the fixed value of the area is larger than the actual drainage range, the calculation result of reservoir pressure is the average pressure within the actual drainage range and the undeveloped range, and the pressure drop rate is slow. If the setting drainage area increases, the range of the reservoir that has not been depressurized increases, resulting in a larger pressure calculation result (Fig.4). However, when the proposed model was used to calculate the coal reservoir pressure, the drainage area changed with the actual water production, and the water production data was used more efficiently. Therefore, the results which were calculated by the proposed model are more realistic.

When the proposed model was used to calculate the average reservoir pressure in the well T1, the pressure drop curve showed a good correspondence with the actual production curve, as seen by the curve in figure.2. From the start of production until 300 days, the reservoir pressure rapidly dropped. Afterward, the reservoir pressure was relatively stable from 300 days to 1200 days. Finally, the reservoir pressure rapidly dropped. The analysis of this pressure curve shows that due to drainage and depressurization, the pressure around the wellbore rapidly dropped in the initial stage, and the drainage range extended from the wellbore to a distant place. In the middle stage, the water and gas production was stable, and the drainage range gradually extended to a distant place. At this time, because the reservoir pressure was constantly replenished from the far well, the average reservoir pressure was maintained at a stable level. In the later period, the EDA was stable, the reservoir pressure rapidly dropped in this area, and the massive desorption of CBM resulted in the rapid increase of gas production.


4.2 Reservoir pressure sensitivity analysis

Coal reservoir pressure is controlled by various factors such as geology, drainage, and engineering (Song et al., 2017; Zhang et al., 2018; Kang et al., 2018). Moreover, engineering factors are uncertain and contingent, and their impact on the reservoir pressure is difficult to assess in a quantitative way (Gu et al., 2017; Wei et al., 2017). The influence of the geological parameters on the reservoir pressure is discussed in this section. Firstly, a typical well was selected as the research object, and its productivity characteristics are actual production curves. Secondly, the four-factor and the three-level orthogonal experiments were designed by selecting the reservoir porosity, irreducible water saturation, Langmuir volume, and Langmuir pressure as the target parameters. Finally, the intuitionistic analysis method was used to analyze the influence of the geological factors on the coal reservoir pressure during the development process.

4.2.1 Orthogonal experimental design

The orthogonal design is one of the most effective and time-saving methods for the studies involving multiple variables to find out which factors (or variables) mostly influence the properties of the target product (Ross, 1988). It is designed by selecting a partial representative combination in all combinations of the experimental factors. Through the analysis of a part of the experimental results, the situation of the comprehensive experiment was studied, and the optimal level combination was realized. The basic feature of the orthogonal experimental design is to replace the comprehensive experiments with some characteristic experiments on one hand, and to study the situation of the comprehensive experiments by analyzing some experimental results on the other (Li, 2005).

In this study, the well T1 is considered as the typical well, and the production characteristic is the production curve of the well T1. The target geological parameters are initial porosity, irreducible water saturation, Langmuir volume, and Langmuir pressure. The initial porosity and the irreducible water saturation control the water content of the coal reservoir, while the Langmuir volume and the Langmuir pressure control the gas content of the coal reservoir. The parameters are independent of each other, and the joint collocation between the parameters has little effect on the experimental results; so, the interaction between the parameters was ignored. Moreover, the ratio of the horizontal component of each parameter is 1:1.5:2 (Table 3) and the orthogonal experiment is designed according to the standard orthogonal array L9 (3

4). The experimental design and experimental results are shown in the follow (Table 4;

Fig.5): Table 3 Experimental factors and horizontal parameters

component (m3) (MPa)

1 20 1 2% 0.4

2 30 1.5 3% 0.6

3 40 2 4% 0.8

Table4 Orthogonal experimental design and experimental results

Test (m3) (MPa)

1 20 1 0.02 0.4 53.75%

2 20 1.5 0.03 0.6 48.52%

3 20 2 0.04 0.8 31.13%

4 30 1 0.03 0.8 21.48%

5 30 1.5 0.04 0.4 59.49%

6 30 2 0.02 0.6 25.53%

7 40 1 0.04 0.6 40.58%

8 40 1.5 0.02 0.8 10.08%

9 40 2 0.03 0.4 39.80%

K1 133.40% 115.81% 89.37% 153.04%

K2 106.50% 118.10% 109.80% 114.63%

K3 90.46% 96.45% 131.20% 62.68%

k1 44.47% 38.60% 29.79% 51.01%

k2 35.50% 39.37% 36.60% 38.21%

k3 30.15% 32.15% 43.73% 20.89%

R 14.32% 7.22% 13.94% 30.12%

(Ki represents the sum of the calculation results of the same horizontal component of the corresponding parameter; ki is the average value of Ki. R indicates the range of the

corresponding parameters which is used to judge the order of the factors affecting the results. Greater range indicates that the factor has a greater influence on the experimental

results. The calculation method of the range is R=max(ki)-min(ki))


Fig.5 Orthogonal experimental calculation results.

4.2.2 Analysis of the results

From the orthogonal experimental results, the influence of the geological factors was analyzed on the coal reservoir depressurization by using the intuitionistic analysis. The intuitionistic analysis solves the problem by comparing the R of each factor. The main factors affecting the experimental results are identified by their R. The results showed that the irreducible water saturation has the greatest influence on the reservoir depressurization, followed by the Langmuir volume, the initial porosity, and finally by the Langmuir pressure. From the corresponding trend of the R, the irreducible water saturation and the Langmuir volume showed negative correlations with the reservoir pressure drop, while the effect of porosity on the reservoir pressure drop showed a positive correlation (Table 4).

Irreducible water saturation and porosity are the key factors that predominate the water content of the coal reservoir as well as the amount of the water production (Li et al., 2018). Larger irreducible water saturation and smaller porosity, suggest weaker water content in the coal reservoir. In the calculation process, the gas and water production curves are actual curves, when the water content of the coal reservoir is relatively weak, the equivalent drainage radius (EDR) is relatively large; i.e. the EDA is also relatively large. Although the reservoir pressure variation was small in the relatively large EDA, the increase of the latter indicates that it has a high production potential. Previous studies have shown that Chinese and American coals are different; indeed, the Chinese coals exhibit relatively higher irreducible water saturation. This could be one of the reasons why there are many CBM wells drilled in the study area of the Qinshui Basin, and the tested CBM wells had relatively high gas contents, yet low gas yield in comparison with those in selected basins of the United States (Fu and Qin, 2003). In this circumstance, the CBM wells in the study area usually feature the early-coming peak of gas production and a short gas production life.

The Langmuir volume is a key factor that controls the gas content of the coal reservoir. Large the Langmuir volume indicates that the adsorption capacity of the coal reservoir is strong. Moreover, when the single well controlled range and the gas production rate are constant, the Langmuir volume is larger and the reservoir pressure drops in a slower rate, indicating that the reservoir has a good production potential. On the contrary, faster drop in the reservoir pressure indicates poorer production potential of coal reservoir. 4.3 Analysis and classification of reservoir depressurization

Based on the above results, and since the proposed reservoir pressure calculation model is more accurate in calculating the average reservoir pressure, some target wells were selected in the Shizhuangnan Block for further calculation; consequently, the wells were classified according to the reservoir depressurization characteristics. However, the reservoir pressure is a key factor in calculating the dynamic changes of the reservoir permeability during development; the calculation results were inputted into the permeability dynamic change model in different wells to study the influence of reservoir pressure on the dynamic changes of coal seam permeability (Chen et al., 2015). The calculation results of the 14 wells in the study area are shown in Table 5. Interestingly, the depressurization of target wells is significantly different (Table 5). The maximum pressure drop can reach 94.22% (well Z3), while the minimum pressure drop is only 17.06% (well T10). The pressure drop curves of the different wells are different in terms of shape and can be specifically divided into "rapidly drop type", "medium-term stability type", and "slowly drop type", which correspond to the "rising type", "rebound type", and "drop type" of the dynamic permeability curve, respectively.

Table 5 Reservoir pressure calculation results

Wells Time (day) (MPa) (MPa) (MPa) (Kpa/100d) Depressurization type

T1 2308 3.30 2.21 33.03% 47.23 medium-term stability type


T3 1503 4.20 2.81 33.10% 94.24 slowly drop type


T5 2044 3.68 0.64 82.60% 148.65 rapidly drop type




T8 1960 3.20 2.14 33.20 % 54.47 slowly drop type



Z1 2622 3.30 0.46 86.06% 108.26 rapidly drop type



Z4 2240 3.35 2.47 26.30% 39.36 slowly drop type

4.3.1 The rapidly drop type

By calculating the reservoir pressure and by analyzing the pressure drop characteristic curve, the production wells having "rapidly drop type" reservoir pressure are T5, Z1, Z2, and Z3. The pressure variation of these wells ranged between 77.7% and 94.2%, and the pressure drop rate ranged between 108.3 and 161.6 KPa/100d. By analyzing the production data, all those wells are classified as high gas-yield production wells, and the average daily water production was relatively low and ranged from 0.5 to 1.5 m

3/d. From the

drainage curve, the gas production characteristics of this type are a short time for the start gas production, which achieves high gas yields, and stable high yields in the later period. The characteristics of water production begin with an initial initial large water production, then rapidly drop in the middle period, and eventually end with basically no water production.

The analysis diagram of the typical well with “rapidly drop type” is shown in figure.6. It clearly reflects the dynamic changes of the reservoir pressure, reservoir permeability, and drainage radius. The reservoir pressure of the typical well tends to drop rapidly during the production process, while the permeability of the reservoir rapidly increases upon a decrease in the reservoir pressure. From the EDR curve, the EDR rapidly increases in the early stage, while the increase rate slows down or even remains constant in the later period. The EDR of the reservoir can be calculated through water production. Such wells have high-water production in the early stage and then rapidly decline, so that the EDR can quickly reach the single well controlled boundary, and pressure interference can be quickly achieved between production wells. Subsequently, the coal reservoir rapidly depressurizes within the EDA and the CBM desorbs in large quantities; hence the production well can quickly and steadily reach high production in the later period. Because of low-water production, high and stable gas production in the later period, the effective stress has little effect on the coal reservoir; in addition, the effect of the matrix shrinkage and gas slippage is far greater than the effective stress, so the reservoir permeability has a "rising type" during the production process.

Fig.6 "The rapidly drop type" typical well production curve.

4.3.2The medium-term stability type

By analyzing the production curve and by calculating the characteristic curve of depressurization, the production wells having "medium-term stability type" reservoir pressure are T1, T2, T4, T6, and T7. The pressure variation of these wells ranged from 33.03% to 51.45%, and the pressure drop rate ranged from 47.23 to 103.03 KPa/100d. According to the production data, most of these wells are classified as medium gas-yield production wells. The average daily gas production and water production ranged from 545.29 to 1064.49 m

3/d and from 1.2 to 2.3 m

3/d, respectively. From the production curve, the gas production characteristics of such wells are

stable low gas-yield after starting gas production in the initial period, and the daily gas production gradually reaches high yield in the later period. The characteristics of water production in such wells are as follow: the water production is high in the early period; it then decreases in the middle period, however, the drop rate is small and basically no water is produced in the later period.

Figure 7 represents an analysis diagram of a typical well with “medium-term stability type”. It can be seen that the average reservoir pressure of the typical well rapidly drops in the early stage, then remains stable for a period, and finally continues to rapidly drop in the later stage. The reservoir permeability rapidly decreases in the early stage, remains stable in the medium stage, and then rapidly increases in the later stage. From the EDR curve, it can be seen that the EDR rapidly increases in the early stage, which is followed by a slower growth rates, nonetheless, it is still increasing. The reason for these results is due to the hydraulic fracture in the near-well zone, the permeability of the reservoir near the production well is high, so the rapid drop of the bottom hole flowing pressure and the large amount of drainage in the early production stage cause the rapid drop of the reservoir pressure in the near-well zone. However,


the drainage area is continuously expanding during the production process on one hand, and the pressure of the outer edge of the reservoir propagates to the drainage area on the other. Consequently, the average pressure of the reservoir is stable for a certain period, which results in low gas production. In the later stage, because of the decrease in the water production, the EDR reaches the well-controlled boundary, the propagation capacity of the reservoir’s outside pressure decreases, and the gas production increases and sustains high gas yields; this makes the reservoir pressure showing a rapid drop. In the early stage, the influence of the effective stress on the reservoir permeability is greater than that of the matrix shrinkage and gas slippage; additionally, the permeability of the reservoir was rapidly reduced as seen by the dynamic change curve of the reservoir permeability. Indeed, this is due to the high -water production and low gas production. During the middle period, and since the water production decreases, the effect of the effective stress reduces damage to the reservoir permeability and renders it stable. Furthermore, and during the later period, the recovery effect of the matrix shrinkage and the gas slippage on the reservoir permeability is greater than the damage effect of the effective stress, result in the gradual increase of the reservoir permeability. This is explained by the increase of the gas production and the decrease of the water production. Therefore, the reservoir permeability is of "rebound type" during the entire production process.

Fig.7 "Medium-term stability type" typical well production curve.

4.3.3 The slowly drop type

The production wells having "slowly drop type" reservoir pressure are T3, T8, T9, T10, and Z4. The pressure variation of these wells ranged from 17% to 33%, and the pressure drop rate ranged from 29 to 94 KPa/100d. By analyzing the production data, all of these wells are classified as low gas-yield production wells. The average daily gas production is less than 500 m

3/d, and the water

production is relatively high. The average daily water production ranged between 1.53 and 2.11 m3/d. From the production curve, it

can be seen that the gas production of such wells is low. However, the daily water production is high and characterized by multiple peaks.

Figure 8 shows an analysis diagram of a typical "slowly drop type" well. It can be seen that the reservoir pressure tends to slowly drop during the production process, while the reservoir permeability rapidly decreases upon the change of the reservoir pressure. Due to the multi-peak shape of the water production in such wells, the EDR rapidly increases during the production process. Therefore, the pressure of the outer edge of the reservoir continuously propagates to the drainage area, and the average reservoir pressure slowly drops, which ultimately leads to low gas production. Because of the production characteristics of “high-water-yield production” and “low-gas-yield production”, the influence of the effective stress of the coal reservoir is greater than that of the matrix shrinkage and the gas slippage; so, the reservoir permeability has a “drop type”.

Fig.8 "Slowly drop type" typical well production curve

5 Conclusions


（1） To accurately calculate the average pressure of the coal reservoir during the development process, we mainly considered the dynamic change of the equivalent drainage area and the self-regulatory effect based on the classic material balance of coalbed methane. The difference between the two models was analyzed by comparing the calculation results between the proposed and the traditional models. The conclusions show that the results calculated by the traditional model are greatly affected by human factors; that is, larger fixed values of the area which is inputted into the formula results in smaller pressure drops in the reservoir. Therefore, the calculated results are untrue. Additionally, when the dynamic change of the EDA isn’t ignored, the EDA in the reservoir pressure prediction model changes with the actual production; indicating a relatively accurate calculated average pressure of the coal reservoir.

（2） The irreducible water saturation, reservoir porosity, Langmuir volume and Langmuir pressure are selected as the target parameters. Additionally, the orthogonal experiment was designed to analyze the influence of the target parameters on the reservoir pressure during the development process. Based on the intuitionistic analysis method, the irreducible water saturation showed the greatest influence on the reservoir pressure, followed by the Langmuir volume, porosity, and finally the Langmuir pressure as seen by the experimental results. The irreducible water saturation and the Langmuir volume are negatively correlated with the reservoir pressure, while the effect of porosity is positively correlated with the reservoir pressure.

（3） Some typical wells were selected to analyze their pressure characteristic curves. The average reservoir pressure that was calculated by the proposed model is inputted into the reservoir permeability prediction model; consequently, the dynamic change of reservoir permeability, during the development process of these wells, was calculated. The pressure drop curves of the different wells were different in shape, and can be specifically divided into "rapidly drop type", "medium-term stability type", and "slowly drop type", which correspond to "rising type", "rebound type", and "drop type" of the dynamic permeability curve, respectively. The reservoir pressure of the “rapidly drop type” production wells greatly drops during the development process, and the reservoir permeability gradually increases. The reservoir pressure of the “slowly drop type” production wells drops to a small extent, and the reservoir permeability gradually decreases. Moreover, the reservoir pressure of the “medium-term stability type” production wells continuously drop in the early and the late stages of the production process, while the reservoir pressure remains stable in the medium-term, correspondingly, the reservoir permeability decreases in the early stage, increases in the later stage, and stabilizes in the medium stage.

Acknowledgements

We would like to thank China United Coalbed Methane Corporation for providing the production well date. This study was

financially supported by the National Science and Technology Major Project of China (Grant No. 2017ZX05064003) and the National Natural Science Foundation of China (Grant No. 41772159/D0208, No.41872178).

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About the first author

YAN Xinlu, male, born in 1993 in Jinzhong City, Shanxi Province; is a Ph. D; he is studying at China University of Geoscience, Beijing; he is mainly

engaged in petroleum and natural gas engineering; currently focuses on the development of coalbed methane.. Email: [email protected].


About the corresponding author

ZHANG Songhang, male, born in 1982 in Nanyang City, Henan Province; Ph. D; graduated from China University of Geoscience, Beijing; associate

professor of China University of Geoscience, Beijing. He is now interested in the study on coalbed methane geology and development. Email: [email protected].

mailto:[email protected]

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The prediction model of coal reservoir pressure and its ... YAN, Songha… · Running title: The prediction model of coal reservoir pressure and its implication The prediction model